MOSCOW — Tens of thousands of Russians embraced the numbing cold and marched to a frozen riverbank near the Kremlin on Saturday, demonstrating their determination to keep up the pressure on Vladimir Putin for fair elections and honest government.

Two months after disputed parliamentary balloting ignited Russia’s first significant protest movement in more than a decade, Saturday’s turnout showed that the demonstrators are not fading away.

In size, the rally was in the same ballpark as two large demonstrations in December; the police said 36,000 came out, the organizers said 120,000.

More determined than they had been at those earlier rallies, which in some ways resembled street fairs, the marchers attacked Putin with gusto. “The longer we freeze here, the longer they’ll freeze in Siberia,” chanted one group as it surged up Bolshaya Yakimanka Street toward Bolotnaya Square, referring to the country’s leadership.

The protesters, from the entire width of the political spectrum, gathered in four columns, one after another. First came the “white-ribbon” group, the apoliticals; then, their order chosen by lot, came liberal democrats, nationalists with their Russian imperial flags, and Communists with their hammer-and-sickle banners.

The segregation seemed to energize each contingent, without engendering name-calling or hostility. “We need a big coalition against Putin,” said one nationalist, Alexander Razumov, 31. “We have no other choice.”

At the same time it emphasized their philosophical differences and raised questions about whether a single leader could emerge to unite them and challenge an entrenched Putin government.

“Power to the millions, not the millionaires,” said Sergei Udaltsov, leader of the Left Front. “We are the millions.”

“Away with the Chekists!” shouted a group of young men, using the name by which KGB officers, such as Putin, liked to call themselves.

Yet it was also clear that a great many protesters had shown up out of a realization that they enjoy the act, and the feelings of solidarity that come with it. That would not be good news to Putin, who has appeared to be holding back in hopes that the movement would run out of steam on its own accord before the March 4 presidential election.

On Saturday, government investigators hit back at the opposition, which has made clean elections one of its central demands. The Investigations Committee charged that most of the videos showing apparent election fraud in December were concocted in the United States and disseminated by a server in California, the Interfax news agency reported. It said the government was determined to discover who was responsible.

Blaming the United States for whatever annoys him in Russia has become a favorite Putin theme. Before the December elections he suggested the country’s only independent election monitor was in the pay of the United States. When the protests began, he accused Secretary of State Hillary Rodham Clinton of signaling the opposition to take to the streets. One protester Saturday carried a sign saying: “I came for free.”

The counter-rally

Organizers friendly to the Kremlin held a competing, counter-rally on Saturday. They called it an “anti-orange” demonstration — an attempt to draw a parallel between the Russian opposition and the instigators of the 2004 Orange Revolution in Ukraine, which was anathema to Putin and which he also blamed on outside intervention.

State-owned Russia Today television announced that 135,000 had attended that rally; the Associated Press put the number at no more than 20,000. Sasha Trusovy, a 23-year-old student, said he and his friends came to the rally because “we don’t want to destroy the country.”

Putin later said he would help pay the fine the organizers incurred because the rally had been so successful it exceeded the 15,000 participants allowed by their permit.

The post office brought in busloads of its workers for the counter-rally, and teachers were recruited from points nearby.

One who chose not to show up was Yulia Konstantinova, a math teacher who turned down a request from her principal and joined the anti-Putin Bolotnaya march instead. “We’re sick and tired of pretending everything is fine,” she said. “It’s not true.”

Saturday was the 22nd anniversary of a huge pro-democracy march in what was then the capital of the Soviet Union. It led directly to the Communist Party’s renunciation of its monopoly on power. Yuri Lobanov, then 52, and a scientist in the Soviet space program, took part that day. “There was more hope back then,” he said. “But look what’s happened. Who could have predicted that a Chekist junta would come to power? I’m ashamed to live in this country.”

In his own field, space, Russia has encountered one failure after another, and he pointed to that as a symptom of rot at the top.

“I have grandchildren and great-grandchildren,” he said. “I want them to live in a free country, where they won’t be cheated. I never thought I’d end my life in such evil times.”

Building ‘civil society’

It was a 20- to 30-minute walk from the gathering place, Oktyabrskaya Square with its huge statue of Lenin, to Bolotnaya. The march and the rally that followed proceeded briskly, on account of the cold. Someday it may be remembered as the jumping rally, as participants kept dancing from one foot to another to keep the blood flowing in their toes.

“It’s a real Russian freeze,” exulted Andrei Sorokin, 25, an engineer and a communist. He was hopping up and down.

“We want to vote against the thieves and crooks, and there are so many in power,” he said. “They’re so confident and arrogant and rude.” Hop and hop and hop. “But you can see on TV how they’ve changed. There’s fear in their eyes.”

Two men carried a 12-foot-long poster board shaped like a condom, because Putin said he mistook the white ribbons worn by protesters for flaccid condoms. On it was written, “We’re protecting ourselves from Putin.”

Political speeches were kept to a minimum. The most electric was delivered by Alexei Navalny, the anti-corruption crusader who has become a favorite of many in the opposition — and a worry for those who distrust his nationalist, occasionally demagogic bent. Yuri Shevchuk

Few said they believed Putin would be defeated in March. Yelena Gorbacheva, a 29-year-old photo editor, said she was concerned that the elections would come off as honest and Putin would win. Then what?

But Mikhail and Marina Kopylov, both 34, said this is just the beginning of a long process.

“We really hope that some kind of movement that can unite us will arise,” Marina said. “People want to be active. They want to be together.”

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